{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:JMIHGOMFTWBU7OWYNKINFA6SAV","short_pith_number":"pith:JMIHGOMF","canonical_record":{"source":{"id":"1904.00294","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-30T21:31:04Z","cross_cats_sorted":[],"title_canon_sha256":"b67fc58ff9b0bef0c9769a6e72e2d364293a3adf25655060907bfb6a815a387c","abstract_canon_sha256":"8cd239f507af26947067b92349b2e5b98fd57c04c0cd5c2363021021c5e1c658"},"schema_version":"1.0"},"canonical_sha256":"4b107339859d834fbad86a90d283d205573c89f793e574248d8fb9072d128b77","source":{"kind":"arxiv","id":"1904.00294","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.00294","created_at":"2026-05-17T23:49:48Z"},{"alias_kind":"arxiv_version","alias_value":"1904.00294v1","created_at":"2026-05-17T23:49:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.00294","created_at":"2026-05-17T23:49:48Z"},{"alias_kind":"pith_short_12","alias_value":"JMIHGOMFTWBU","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"JMIHGOMFTWBU7OWY","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"JMIHGOMF","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:JMIHGOMFTWBU7OWYNKINFA6SAV","target":"record","payload":{"canonical_record":{"source":{"id":"1904.00294","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-30T21:31:04Z","cross_cats_sorted":[],"title_canon_sha256":"b67fc58ff9b0bef0c9769a6e72e2d364293a3adf25655060907bfb6a815a387c","abstract_canon_sha256":"8cd239f507af26947067b92349b2e5b98fd57c04c0cd5c2363021021c5e1c658"},"schema_version":"1.0"},"canonical_sha256":"4b107339859d834fbad86a90d283d205573c89f793e574248d8fb9072d128b77","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:48.867867Z","signature_b64":"/UNa83hzPVE018YgiPr7HJOKPp6pRxqpWKtPVF8ae7eq/76arjTvKJfGfrbmQyuO9JTojYKWggDn1cdZNPeIDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b107339859d834fbad86a90d283d205573c89f793e574248d8fb9072d128b77","last_reissued_at":"2026-05-17T23:49:48.867349Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:48.867349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.00294","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:49:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+W6t2u4CyUQ/wnOPhULuAybalWgL7hAvGT4ZiCEisQFMCTeAu/hvzrEkJjyIISCzpeYknDJd8kd00MMBn8b5Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T06:50:46.028254Z"},"content_sha256":"fd236bb47cf0ed9f95d901fbddd507d8b9d2e8d6288a695b422430b886c8a6e2","schema_version":"1.0","event_id":"sha256:fd236bb47cf0ed9f95d901fbddd507d8b9d2e8d6288a695b422430b886c8a6e2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:JMIHGOMFTWBU7OWYNKINFA6SAV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Growth in the Muskat problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Omar Lazar, Rafael Granero-Belinch\\'on","submitted_at":"2019-03-30T21:31:04Z","abstract_excerpt":"We review some recent results on the Muskat problem modelling multiphase flow in porous media. Furthermore, we prove a new regularity criterion in terms of some norms of the initial data in critical spaces ($\\dot{W}^{1,\\infty}$ and $\\dot{H}^{3/2}$)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.00294","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:49:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aU4LN2gyUy1BUl7BUwVDjzq5+j6Yu6BRkUa4zQdS8WsA8mrozRWZRV7sJPrsV8R4Xa5/J96ffIeI8bhOOFGRDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T06:50:46.028956Z"},"content_sha256":"7179a9c804e6cdc2a51186fe029279c246452c64ff3738c9cb7a3d53c99f05c7","schema_version":"1.0","event_id":"sha256:7179a9c804e6cdc2a51186fe029279c246452c64ff3738c9cb7a3d53c99f05c7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JMIHGOMFTWBU7OWYNKINFA6SAV/bundle.json","state_url":"https://pith.science/pith/JMIHGOMFTWBU7OWYNKINFA6SAV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JMIHGOMFTWBU7OWYNKINFA6SAV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T06:50:46Z","links":{"resolver":"https://pith.science/pith/JMIHGOMFTWBU7OWYNKINFA6SAV","bundle":"https://pith.science/pith/JMIHGOMFTWBU7OWYNKINFA6SAV/bundle.json","state":"https://pith.science/pith/JMIHGOMFTWBU7OWYNKINFA6SAV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JMIHGOMFTWBU7OWYNKINFA6SAV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:JMIHGOMFTWBU7OWYNKINFA6SAV","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8cd239f507af26947067b92349b2e5b98fd57c04c0cd5c2363021021c5e1c658","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-30T21:31:04Z","title_canon_sha256":"b67fc58ff9b0bef0c9769a6e72e2d364293a3adf25655060907bfb6a815a387c"},"schema_version":"1.0","source":{"id":"1904.00294","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.00294","created_at":"2026-05-17T23:49:48Z"},{"alias_kind":"arxiv_version","alias_value":"1904.00294v1","created_at":"2026-05-17T23:49:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.00294","created_at":"2026-05-17T23:49:48Z"},{"alias_kind":"pith_short_12","alias_value":"JMIHGOMFTWBU","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"JMIHGOMFTWBU7OWY","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"JMIHGOMF","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:7179a9c804e6cdc2a51186fe029279c246452c64ff3738c9cb7a3d53c99f05c7","target":"graph","created_at":"2026-05-17T23:49:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We review some recent results on the Muskat problem modelling multiphase flow in porous media. Furthermore, we prove a new regularity criterion in terms of some norms of the initial data in critical spaces ($\\dot{W}^{1,\\infty}$ and $\\dot{H}^{3/2}$).","authors_text":"Omar Lazar, Rafael Granero-Belinch\\'on","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-30T21:31:04Z","title":"Growth in the Muskat problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.00294","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:fd236bb47cf0ed9f95d901fbddd507d8b9d2e8d6288a695b422430b886c8a6e2","target":"record","created_at":"2026-05-17T23:49:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8cd239f507af26947067b92349b2e5b98fd57c04c0cd5c2363021021c5e1c658","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-30T21:31:04Z","title_canon_sha256":"b67fc58ff9b0bef0c9769a6e72e2d364293a3adf25655060907bfb6a815a387c"},"schema_version":"1.0","source":{"id":"1904.00294","kind":"arxiv","version":1}},"canonical_sha256":"4b107339859d834fbad86a90d283d205573c89f793e574248d8fb9072d128b77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b107339859d834fbad86a90d283d205573c89f793e574248d8fb9072d128b77","first_computed_at":"2026-05-17T23:49:48.867349Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:48.867349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/UNa83hzPVE018YgiPr7HJOKPp6pRxqpWKtPVF8ae7eq/76arjTvKJfGfrbmQyuO9JTojYKWggDn1cdZNPeIDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:48.867867Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.00294","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd236bb47cf0ed9f95d901fbddd507d8b9d2e8d6288a695b422430b886c8a6e2","sha256:7179a9c804e6cdc2a51186fe029279c246452c64ff3738c9cb7a3d53c99f05c7"],"state_sha256":"01f997e9372288a76bccc4c2ad5cf6dce75329e961c8531d14757347aeb5caf6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S+DkejNZEDuJP6QT6zRk9pn737QthWqrlvEEIXmZG/rBmkx7/ek98oBvqe4Iu+pCuHNJvKFPZ7bgACQNq3kZBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T06:50:46.032569Z","bundle_sha256":"9d4fc5c04e763d3b63b80547167ea284742efb99173977f6e9f93f44108c80dc"}}